November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 10 Apr 2012
Posts: 269
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)

We are given two integers a and b, such that, 2 < a < b and b is not a
[#permalink]
Show Tags
01 Apr 2013, 00:05
Question Stats:
39% (02:33) correct 61% (02:30) wrong based on 164 sessions
HideShow timer Statistics
We are given two integers a and b, such that, 2 < a < b and b is not a multiple of a. Is the remainder of the division of b by a greater than 1? (1) The least common multiple of a and b is 42 (2) The greatest common factor of a and b is 2
Official Answer and Stats are available only to registered users. Register/ Login.



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 612

Re: We are given two integers a and b, such that, 2 < a < b and b is not a
[#permalink]
Show Tags
01 Apr 2013, 00:54
guerrero25 wrote: We are given two integers a and b, such that, 2 < a < b and b is not a multiple of a. Is the remainder of the division of b by a greater than 1? (1) The least common multiple of a and b is 42 (2) The greatest common factor of a and b is 2 I am struggling in this type of questions ..Any help is greatly appreciated. thanks! From F.S 1 , for a=6,b=7, we have the remainder as 1, which is not more than 1. Again, for a=3,b=14, we have a remainder as 2, which is more than 1. Insufficient. From F.S 2, the integers a and b are of the form 2x and 2y, where x and y are coprimes. Also, 2y = 2x*q + R, where q is a nonnegative integer. or R = 2(yqx). As x and y are coprimes, thus y is not equal to qx, for any integral value of q. Thus, (yqx) will never be zero. And as R is always positive, the value of R will always be more than 1. Sufficient. Note that as a>2, we can have the first value of a only as 4. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Director
Status: Tutor  BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
Location: India
Concentration: Finance, Marketing
GPA: 3
WE: Information Technology (Computer Software)

Re: We are given two integers a and b, such that, 2 < a < b and b is not a
[#permalink]
Show Tags
01 Apr 2013, 01:03
guerrero25 wrote: We are given two integers a and b, such that, 2 < a < b and b is not a multiple of a. Is the remainder of the division of b by a greater than 1? (1) The least common multiple of a and b is 42 (2) The greatest common factor of a and b is 2 I am struggling in this type of questions ..Any help is greatly appreciated. thanks! STAT1 is not sufficient as we can have mutiple cases case 1 a=6, b=7 now remainder when b is divided by a will be 1 which is NOT greater than 1 case 2 a=6, b=14 now reaminder when b is divided by a will be 2 which is greater than 1 So, STAT1 is NOT sufficient STAT2 GCD of a and b is 2 means that both a and b are even numbers And we know that b is not a mutiple of a so, in any case reamindder when b is divided by a will be more than 1 case1 a=4, b=6 remaidner will be 2 greater than 1 case 2 a=6, b=10 reaminder will be 4 greater than 1 Also, if you notice then the reaminder is a even number greater than or equal to 2 So STAT2 is SUFFICIENT hence, answer will be B Hope it helps!
_________________
Ankit
Check my Tutoring Site > Brush My Quant
GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief
How to Solve : Statistics  Reflection of a line  Remainder Problems  Inequalities



SVP
Joined: 06 Sep 2013
Posts: 1744
Concentration: Finance

Re: We are given two integers a and b, such that, 2 < a < b and b is not a
[#permalink]
Show Tags
01 Apr 2014, 05:26
Alright, as Hamilton Lin says, let's do it!
Statement 1 tells us that the LCM of (a,b) is 42. Therefore, we have that b=7,a=6 remainder is 1, but if b=14 and a=3 remainder is 2, therefore two different answers–> Insufficient.
Statement 2, says that the GCF of (a,b) is 2. Therefore since both are even and b is not a multiple of a the remainder will always be 2, therefore Sufficient
B is the correct answer
Cheers J



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Re: We are given two integers a and b, such that, 2 < a < b and b is not a
[#permalink]
Show Tags
21 Mar 2018, 00:19
Solution: We are given: • ‘\(b\)’ is not a multiple of ‘\(a\)’.
• Both, ‘\(a\)’ and ‘\(b\)’, are greater than \(2\) and ‘\(b\)’ is greater than ‘\(a\)’. Statement1 is “The least common multiple of ‘a’ and ‘b’ is 42”.\(42= 2*3*7\) ‘\(a\)’ and ‘\(b\)’ can have multiple values based on prime factorization of \(42\). Since the value of remainder may or may not greater than 1. Hence, Statement 1 alone is not sufficient to answer the question. Statement2 is “The greatest common factor of ‘a’ and ‘b’ is 2.”Thus, • \(a=2x\) and \(b=2y\), where \(x\) and \(y\) are coprime numbers. Since ‘\(b\)’ is greater than ‘\(a\)’, ‘\(b\)’ on dividing by ‘\(a\)’ can be written as: • \(2y= 2x*m + r\), where ‘\(r\)’ is the remainder and ‘\(r\)’ cannot be ‘\(0\)’ as ‘\(b\)’ is not a multiple of ‘\(a\)’.
• Since \(2y\) is an even number, \((2x*m + r)\) should be an even number.
o ‘\(r\)’ must be even.
Thus, the least value of ‘\(r\)’ can be \(2\). Hence, Statement 2 alone is sufficient to answer the question. Answer: B
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com




Re: We are given two integers a and b, such that, 2 < a < b and b is not a &nbs
[#permalink]
21 Mar 2018, 00:19






